This form is usually translated as "regardless"; however its meaning seems to be pretty similar to をよそに and to をものともせず. Is their usage different?
Grammatically, ～をよそに, ～をものともせず and ～にも構わず work similarly. However there is a difference in meaning.
- 構う can mean "to worry about", "to look after", etc. Thus ～に構わず tends to be used for something/someone people should normally care about, such as a dying ally and an advice of your friend. も adds the nuance of "even".
- When you use ～をものともせず, the target is normally a direct obstacle or hardship you should endure, such as a storm, an enemy attack and a torture. It's used to describe the strength or boldness of the subject.
- 余所【よそ】 means "other (irrelevant) places". ～をよそに means the speaker is not interested in something at all in the first place.